InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A uniform magnetic field of `3000G` is established along the positive z-direction. A rectangular loop of sides `10cm` and `5cm` carries a current `12A`. What is the torque on the loop in the different cases shown in the figure. What is the force on each case? Which case corresponds to stable equilibrium? |
|
Answer» Magnetic field strength, `B = 3000G = 3000 xx 10^(-4)T = 0.3T` Length of the rectangular loop, `l = 10cm` Width of the rectangular loop, `b = 5cm` Area of the loop, ` A= l xx b = 10 xx 5 = 50 cm^(2) = 50 xx 10^(-4)m^(2)` Current in the loop, `I = 12A` Now, taking the anti-clockwise direction of the current as positive and vise-versa: (a) Torque, `vec(tau) = I vec(A) xx vec(B)` From the given figure, it can be observed that A is normal to the y-z plane and B is directed along the z-axis. `:. r = 12 xx (50 xx 10^(-4)) hati xx 0.3 hatk` `=-0 1.8 xx 10^(-2)hatj Nm` The torque is `1.8 xx 10^(-2)Nm` along the negative y-direction. The force on the loop is zero because the angle between A and B is zero. (b) This case is similar to case (a). Hence, the answer is the same as(a). (c) Torque `tau = IA xx B` From the given figure, it can be observed that A is normal to the x-z plane and B is directed along the z-axis. `:. tau = - 12 xx (50 xx 10^(-4))hatj xx 0.3 hatk` `=- 1.8 xx 10^(-2)hatj Nm` The torque is `1.8 xx 10^(-2)Nm` along the negative x direction and the force is zero. (d) Magnitude of torque is given as: `|tau| = IAB` `= 12 xx 50 xx 10^(-4) xx 0.3` `= 1.8 xx 10^(-2)Nm` ltbr. Torque is `1.8 xx 10^(-2)Nm` at an angle of `240^(@)` with positive x direction. The force is zero. (e) Torque `tau = l vec(A) xx vec(B)` `= (50 xx 10^(-4) xx 12) hatk xx 0.3 hatk = 0` Hence, the torque is zero. The force is also zero. (f) torque `tau = l vec(a) xx vec(B)` `=(50 xx 10^(-4) xx 12) hatk xx 0.3 hatk =0` Hence, the torque is zero. The force is also zero. In case (e), The direction of `I vec(A)` and `vec(B)` is the same and the angle between them is zero. If displaced, they come back to an equilibrium. hence, its equilibrium is stable. Whereas, in case (f), the direction of `I vec(A)` and `vec(B)` is opposite. The angle between them is `180^(@)`. If disturbed, it does not come back to its original position. Hence, its equilibrium is unstable. |
|